Generally, a display system for displaying an image is divided broadly into direct-view picture display systems represented by CRTs (Cathode Ray Tubes) and projection systems having projectors for displaying an image on a screen (hereinafter referred to as "projectors"). With projectors, an image is magnified via a projection lens and is displayed on a screen. When the projector is not centered or cannot be centered on the screen, i.e., the lens is not at a 90.degree. angle to the center of the screen, the resulting projected image is distorted or skewed. This phenomenon is known in the art as keystoning. With keystoning, an asymmetrical image is projected onto the screen. In other words, the image projected onto the screen has a trapezoidal shape (keystone) as opposed to a rectangular shape.
FIG. 1 illustrates a projector 10 having a projection lens 12 at a 90.degree. angle to the center of a screen 14 resulting in image 16 which is projected in the shape of a rectangle onto screen 14 without keystoning or trapezoidal distortion or skewing as shown in FIG. 2. As shown in FIGS. 1 and 2, a center axis 18 is a line connecting a point 20 lying on the surface plane of screen 14 and a center point 22 of projection lens 12 of projector 10. Center axis 18 forms an upward/downward projection angle A and a right/left projection angle B with the surface of screen 14. When projection angles A and B are 90.degree. as shown in FIGS. 1 and 2, projector 10 and projection lens 12 are said to be "centered" or at a 90.degree. projection angle to screen 14. Projection angles A and B are referred to as upward/downward and right/left projection angles, respectively, since center point 22 of projection lens 12 is either below/above point 20 or to the right/left of point 20, respectively.
Referring now to FIGS. 3 and 4 wherein reference numerals or letters which are like, similar, or identical to reference numerals or letters used in FIGS. 1 and 2 indicate like, similar, or identical components or features. Here, upward/downward projection angle A and/or right/left projection angle B are not equal to 90.degree. resulting in image 16 being projected in the shape of a trapezoid onto screen 14 with keystoning.
In U.S. Pat. No. 5,664,858 (incorporated herein by reference), Woo discloses an apparatus and method for pre-compensating an asymmetrical picture in a projection system to correct keystoning when a projection lens of a projector is arranged at an upward or downward projection angle relative to a screen. The apparatus and method disclosed are implemented in a hardware intensive configuration shown in FIG. 7 therein. With presentation systems utilizing a computer and a software application, such as Power Point (Power Point is a trademark of Microsoft Corporation), to generate and store images and a projector (such as manufactured and sold by Boxlight Corporation or Epson America, Inc.) which interfaces with the computer to project the computer-generated images on a screen, modifing the computer or projector to include the hardware solution proposed by Woo to correct keystoning is not practical. Also, the hardware solution proposed by Woo does not correct keystoning caused by a projection lens of a projector being arranged at projection angles other than an upward/downward projection angle, such as right/left projection angles or a combination of a right/left projection angle and an upward/downward projection angle. What is needed is a software solution for such a presentation system to correct keystoning, without having to center the projector on the screen, to avoid the need to modify the computer's or projector's hardware and to correct keystoning caused by projection angles other than an upward/downward projection angle.